We investigate how nanospaces surrounded by a 10-membered ring of ZSM-5 zeolite affect the reaction intermediates formed during dioxygen activation by enclosed dicopper cations. Two types of dioxygen intermediates are considered: one is an O-2 center dot center dot center dot Cu-2 complex, where dioxygen binds to the two Cu cations, and the other is a bis(mu-oxo)dicopper complex converted from an O-2 center dot center dot center dot Cu-2 complex by the cleavage of the O-O bond. We employ large-scale density functional theory (DFT) calculations with the B3LYP functional to examine the energetics of the two dioxygen intermediates inside a 10-membered ring of ZSM-5 with double Si -> AI substitutions at variable locations. The properties of the O-2 center dot center dot center dot Cu-2 complexes, such as the dioxygen bridging modes and dioxygen activation, are strongly affected by the locations of the two AI atoms within the 10-membered ring. In particular, the O-2 center dot center dot center dot Cu-2 complexes have either end-on or side-on bridging modes depending on the substituted AI positions. On the other hand, the steric hindrances of a ZSM-5 cavity play crucial roles in determining the properties of the bis(mu-oxo)dicopper complexes containing a diamond Cu2O2 core. By restricting its Cu2O2 core to a 10-membered ring of ZSM-5 in which the two Al atoms are second-nearest neighbors, each Cu cation is tetrahedral four-coordinate. On the other hand, the Cu cations have almost square planar coordination inside a ZSM-5 where the Al atoms are fourth-nearest neighbors. The different Cu coordination environments are responsible for the different levels of stability; the planar diamond Cu2O2 core is 30.7 kcal/mol more stable relative to the tetrahedral case. Since the ZSM-5 nanospaces directly influence the stability of the bis(mu-oxo)dicopper complexes by changing the Cu coordination environments, zeolite confinement effects on the bis(mu-oxo)dicopper complexes are more noticeable than those in the O-2 center dot center dot center dot Cu-2 cases. The DFT findings are important in terms of catalytic functions, because the spatial constraint from the ZSM-5 should significantly contribute to the stability of the reaction intermediates formed during the dioxygen activation.